Kamal Belkebir

Special section: Testing inversion algorithms against experimental data

An introduction to the special section is given. The new database of experimental data used in this section is also introduced. This database can be accessed from this articles Multimedia Enhancements page.

Microwave imaging-Location and shape reconstruction from multifrequency scattering data

The problem of determining the shape and location of an object embedded in a homogeneous dissipative medium from measurements of the field scattered by the object is considered in this paper. The object is assumed to be an infinite cylinder of known cross section illuminated by a TM plane wave and the scattered field is measured on a line segment perpendicular to the direction of incidence. Measurement data are carried out at three different frequencies for a homogeneous cylinder of known dielectric constant. The location and contour shape are determined using two different reconstruction algorithms, a Newton-Kantorovich (NK) method and the modified gradient (MG) method whose effectiveness and robustness are compared. Both methods are based on domain integral representations of the field in the body. They involve an iterative minimization of the defect between an integral representation of the field measured on the line and the actual measured data. The NK method involves a linearization of the nonlinear relation between the field and the contrast, as well as the solution of a direct scattering problem at each iteration. The MG method seeks the simultaneous reconstruction of the field and the characteristic function of the support of the scatterer without solving a direct problem at each step. Both methods employed the same initial guess and the a priori information that the characteristic function is nonnegative.

Validation of 2d iNverse Scattering Algorithms From Multi-Frequency Experimental Data

Reconstructions of two dimensional dielectric or conducting objects from multi-frequency experimental data are considered in the present paper. Two different iterative methods are used for solving the inverse scattering problem. The first one is based on a boundary integral formalism and retrieves boundaries and complex permittivities of unknown homogeneous scatterers. For this method initial guesses are derived from method of decomposition of the time reversal operator (DORT) combined with a low frequency approximation. The second method is based on a domain integral formalism and retrieves the relative complex permittivity distribution inside some investigated domain. The data were carried out in a controlled environment (anechoic chamber) and the reconstructions have been performed using multifrequency approach, i.e., the scheme starts with the lowest available frequency and uses the final result as initial guess at higher frequency in order to enhance the resolution.

Tomographic diffractive microscopy: basics, techniques and perspectives

Tomographic diffractive microscopy (TDM) is an advanced digital imaging technique, which combines the recording of multiple holograms with the use of inversion procedures to retrieve quantitative information on the sample. In this review, we discuss the basic theory of TDM in the framework of electromagnetism and draw a comparison with conventional widefield microscopes. We describe various implementations of TDM, highlighting their power of resolution. Finally, we present some research perspectives for increasing the potential of this promising new imaging modality.

Superresolution in total internal reflection tomography

We simulate a total internal reflection tomography experiment in which an unknown object is illuminated by evanescent waves and the scattered field is detected along several directions. We propose a full-vectorial three-dimensional nonlinear inversion scheme to retrieve the map of the permittivity of the object from the scattered far-field data. We study the role of the solid angle of illumination, the incident polarization, and the position of the prism interface on the resolution of the images. We compare our algorithm with a linear inversion scheme based on the renormalized Born approximation and stress the importance of multiple scattering in this particular configuration. We analyze the sensitivity to noise and point out that using incident propagative waves together with evanescent waves improves the robustness of the reconstruction.

Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography

Optical diffraction tomography is an imaging technique that permits retrieval of the map of permittivity of an object from its scattered far field. Most reconstruction procedures assume that single scattering is dominant so that the scattered far field is linearly linked to the permittivity. In this work, we present a nonlinear inversion method and apply it to complex three-dimensional samples. We show that multiple scattering permits one to obtain a power of resolution beyond the classical limit imposed by the use of propagative incident and diffracted waves. Moreover, we stress that our imaging method is robust with respect to correlated and uncorrelated noise.

Localization and characterization of two-dimensional targets buried in a cluttered environment

In the present paper, we consider a two-dimensional inverse scattering problem involving two semi-infinite media separated by an interface. The targets under test are assumed to be buried in one of the two media while the sources and the receivers are located in the other medium (limited-aspect data configuration). We present an iterative scheme to reconstruct the permittivity distribution of the unknown object. This method consists in building up a sequence of the parameter of interest by minimizing, at each iteration step, a cost functional representing the discrepancy between the data and those that would be obtained with the best available estimation of the parameter. In addition, when clutter is present, the decomposition of the time reversal operator method is used to improve the signal-to-clutter ratio, since it allows us to synthesize a wave that focuses on the scatterer. The data associated with this incident field are included in the iterative minimization procedure.

Modified² gradient method and modified Born method for solving a two-dimensional inverse scattering problems

This paper concerns the reconstruction of the complex relative permittivity of an inhomogeneous object from the measured scattered field. The parameter of interest is retrieved using iterative techniques. Four methods are considered, in which the permittivity is updated along the standard Polak–Ribiere conjugate gradient directions of a cost functional. The difference lies in the update direction for the field, and the determination of the expansion coefficients. In the modified gradient method, the search direction is the conjugate gradient direction for the field, and the expansion coefficients for field and profile are determined simultaneously. In the Born method (BM) the field is considered as the fixed solution of the forward problem with the available estimate of the unknown permittivity, and only the profile coefficients are determined from the cost function. In the modified Born method, we use the same field direction as in the BM, but determine the coefficients for field and profile simultaneously. In the modified2 gradient method, we use both field directions, and again update all coefficients simultaneously. Examples of the reconstruction of either metal or dielectric cylinders from experimental data are presented and the methods are compared for a range of frequencies.

Multiple-frequency distorted-wave Born approach to 2D inverse profiling

The present paper deals with the inversion from experimental data provided by Institut Fresnel, France. The distorted-wave Born iterative approach is applied to the reconstruction of two lossless configurations involving dielectric circular cylinders. The dynamic range and the resolution of this scheme are governed by the operating frequency. For a low frequency, the dynamic range is large and the resolution is limited; raising the frequency improves the resolution at the cost of dynamic range. To obtain a high resolution for a large contrast, scattered-field information at multiple frequencies can be used. This is demonstrated for two cases where a direct inversion does not lead to convergence.

High-resolution optical diffraction microscopy

In an optical diffraction microscopy experiment, one measures the phase and amplitude of the field diffracted by the sample and uses an inversion algorithm to reconstruct its map of permittivity. We show that with an iterative procedure accounting for multiple scattering, it is possible to visualize details smaller than lambda/4 with relatively few illumination and observation angles. The roles of incident evanescent waves and noise are also investigated.